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1. Solve the following equation. Determine whether the equation is an
identity, conditional equation, or an inconsistent equation: 3 – 5(2x + 1) 2(x – 4) = 0
{1/4}; identity equation
{1/6}; inconsistent equation
{1/9}; conditional equation
{1/2}; conditional equation
2. Find the slope of the line passing through each pair of points or state
that the slope is undefined: (0, a) and (b, 0)
m = – a/b
Undefined
m = a/b
m = – a/ab
3. Find the slope of the line passing through each pair of points or state
that the slope is undefined: (a, b) and (a, b + c)
= –b/abc
= b/ab
Undefined slope
= a/abc
4.
Find all the zeros of each polynomial function and write the polynomial as a
product of linear factors.
-2, 1/2, +- i ; f(x) = (x – i)(x + i)(x + 2)(2x – 1)
2, 1/2, +- i ; f(x) = (x – i)(x – i)(x + 2)(2x – 1)
-2, 1/2, +- i ; f(x) = (x + i)(x + i)(x + 2)(2x – 1)
-1, 1/2, +- i ; f(x) = (x – i)(x + i)(x + 2)(2x + 1)
5.
Solve the following exponential equation. Express the solution set in terms of
natural logarithms or common logarithms to a decimal approximation, of two
decimal places, for the solution:
{ ln 10, 478 + 3/5}; ˜ 2.45
{ ln 10, 376 + 3/5}; ˜ 1.78
{ ln 12, 402 + 2/5}; ˜ 2.16
{ ln 10, 277 + 3/8}; ˜ 1.57
6.
Solve the following system:
{(2, -3), ( -1, 4)}
{(4, -8), ( -2, 4)}
{(1, -2), ( -2, 9)}
{(4, -3), ( -3, 4)}
7.
Solve the following system of equations using matrices: x + 2y – z = -3 2x – 4y
+ z = -7 -2x + 2y – 3z = 4
{(-4, 1/2, 0)}
{(-3, 1/2, 1)}
{(-2, 1/2, -1)}
{(3, 1/2, 2)}
8.
Locate the foci and find the equations of the asymptotes.
foci: (1, -1+-2v4); asymptotes: (y + 2) = 1/2 (x – 2)
foci: (1, -2+-2v3); asymptotes: (y + 2) = 1/2 (x – 2)
foci: (1, -2+-2v5); asymptotes: (y + 2) = 1/2 (x – 1)
foci: (1, -2+-2v7); asymptotes: (y + 2) = 1/2 (x – 2)
9.
Locate the foci and find the equations of the asymptotes: (x – 1)2- (y – 2)2 = 3
foci: (1 {16, 2); asymptotes: (y – 2) = {(x – 1)
foci: (1 {12, 2); asymptotes: (y – 3) = {(x – 3)
foci: (1 {12, 2); asymptotes: (y – 1) = {(x – 1)
foci: (1 {14, 2); asymptotes: (y – 2) = {(x – 1)
10.
In a class of 50 students, 29 are Democrats, 11 are business majors, and 5 of
the business majors are Democrats. If one student is randomly selected from
the class, find the probability of choosing: (a) Democrat who is not a business
major. (b) A student who is neither a Democrat nor a business major.
a. 11/25 b. 4/10
a. 12/25 b. 3/10
a. 9/25 b. 6/10
a. 7/25 b. 5/10
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